The present invention relates in general to quantum computing, and more specifically to efficient reduction of resources for the simulation of fermionic Hamiltonians on quantum hardware.
In particle physics, a fermion is any particle characterized by Fermi-Dirac statistics. These particles obey the Pauli Exclusion Principle. Fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose-Einstein statistics. A fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. According to the spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.
In addition to a spin characteristic, fermions also possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin statistics relation is in fact a spin statistics-quantum number relation. As a consequence of the Pauli Exclusion Principle, only one fermion can occupy a particular quantum state at any given time. If multiple fermions have the same spatial probability distribution, at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles, although in the current state of particle physics the distinction between the two concepts is unclear. Weakly interacting fermions can also display bosonic behavior under extreme conditions. At low temperatures, fermions show superfluidity for uncharged particles and superconductivity for charged particles. Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter.